"We didnâ€™t expect that result... itâ€™s better than them winning," Giggs, after hearing of Chelsea's 0-1 slip-up, told MUTV.
"Weâ€™ve got to do our own job, not worry about the teams around us. Itâ€™s still in our hands."
That said, Giggs wasn't taking defeat at Fulham lightly, especially as it confirmed back-to-back defeats in the league for the first time since the 2004/05 season.
"Weâ€™re obviously disappointed with the result. After losing last weekend, we wanted to come here and put on a good performance.
"We didnâ€™t do that in the first half - our passing was sloppy and our movement wasnâ€™t good enough. We just couldnâ€™t get it going, the tempo wasnâ€™t good."
Giggs had praise for goalkeeper Edwin van der Sar on his return to Craven Cottage.
He added: "Going a goal behind and down to ten men, we had to arrange our shape a little bit differently. We came out and played a lot better in the second half. We were on top, we created some good chances and their keeper made a couple of good saves. Had one of those efforts gone in then we could have gone on to win it but it wasnâ€™t to be.
"Some of our lads now go away for the international break. Hopefully we wonâ€™t have any injuries and we can get back on track against Villa."